Three New Genuine Five-valued Logics Intended to Model Non-trivial Concepts

Abstract

We introduce three 5-valued paraconsistent logics that we name FiveASP1, FiveASP2 and FiveASP3. Each of these logics is genuine and paracomplete. The new value is called e attempting to model the notion of ineffability. If one drops e from any of these logics one obtains a well known 4-valued logic introduced by Avron. If, on the other hand one drops the “implication” connective from any of these logics, one obtains Priest logic FDEe. We present some properties of these logics.